Answer:
A) C1 = 0.00187 m = 0.187 cm,  C2 = 0.0062 m = 0.62 cm
B)  A sample of how the graph looks like is attached below ( periodic sine wave ) 
C) w = ![\sqrt[4]{3}](https://tex.z-dn.net/?f=%5Csqrt%5B4%5D%7B3%7D) is when the amplitude of the forced response is maximum
 is when the amplitude of the forced response is maximum
Step-by-step explanation:
Given data :
mass = 5kg 
length of spring = 10 cm = 0.1 m 
f(t) = 10sin(t) N 
viscous force = 2 N 
speed of mass = 4 cm/s = 0.04 m/s
initial velocity = 3 cm/s = 0.03 m/s
Formulating initial value problem 
y = viscous force / speed = 2 N / 0.04 m/s = 50 N sec/m
spring constant = mg/ Length of spring = (5 * 9.8) / 0.1 = 490 N/m
f(t) = 10sin(t/2) N 
using the initial conditions of u(0) = 0 m and u"(0) = 0.03 m/s to express the equation of motion 
the equation of motion = 5u" + 50u' + 490u = 10sin(t/2)
A) finding the solution of the initial value 
attached below is the solution and 
B) attached is a periodic sine wave replica of how the grapgh of the steady state solution looks like 
C attached below